Derivation and stability analysis of the analytical structures of the interval type-2 fuzzy PID controller

Adaptive Fuzzy Type-2 in Control of 2-DOF Helicopter

“…However, guaranteeing a robust interval fuzzy type-2 and proofing its stability is yet a big challenge objective for researchers because of its complicated structure, therefore the information taken from the (FOU) is used to develop some membership functions conditions which through them we can handle the stability analysis where the FOU here gives us the chance to generate different stages of nonlinear control curves to use while also providing a certain robustness which cannot found in type-1 [22]. Different approaches were used to realize the stability in fuzzy type-2, the wellknown Lyapunov based approach [22] and the other is the bounded input bounded output (BIBO) based approach [23] Consider the system shown in Fig. 5 Regarding to (31) and (32) as stability conditions and according to the small gain theorem, that any bounded input pair (u 1 , u 2 ) generates a bounded output pair (y 1 , y 2 ), the system is BIBO stable if y 1 y 2 < 1 [23].…”

“…Different approaches were used to realize the stability in fuzzy type-2, the wellknown Lyapunov based approach [22] and the other is the bounded input bounded output (BIBO) based approach [23] Consider the system shown in Fig. 5 Regarding to (31) and (32) as stability conditions and according to the small gain theorem, that any bounded input pair (u 1 , u 2 ) generates a bounded output pair (y 1 , y 2 ), the system is BIBO stable if y 1 y 2 < 1 [23]. IV.…”

Embedded intelligent adaptive PI controller for an electromechanical system

“…A T2-FS is characterized by a fuzzy membership function, unlike a T1-FS where the membership grade is a crisp number in [0, 1] [29]. The conventional PID controller is combined with an interval type-2 fuzzy logic system (IT2-FLS) in order to achieve better system performance over the conventional PID controller with type-1 FLS [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Although favorable performance can be obtained, these controllers are limited on tuning the controller parameters related to uncertain systems.…”

Intelligent Tracking Control Using Pso-Based Interval Type-2 Fuzzy Logic for a Mimo Maneuvering System

“…2 ‖ ≤ 2. ‖ 2 ‖ + Γ2 (25) According to the theorem of small Gain, which illustrates that any bounded output pair (y1, y2) is generated by any bounded input pair (Z1, Z2), and to the stability conditions in equations (24 and 25), the system is BIBO stable if y1.y2 1 [23].…”